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Decomposition of \( S_{8}^{\mathrm{new}}(2) \) into irreducible Hecke orbits

magma: S := CuspForms(2,8);
magma: N := Newforms(S);
sage: N = Newforms(2,8,names="a")
Label Dimension Field $q$-expansion of eigenform
2.8.1.a 1 \(\Q\) \(q \) \(\mathstrut-\) \(8q^{2} \) \(\mathstrut+\) \(12q^{3} \) \(\mathstrut+\) \(64q^{4} \) \(\mathstrut-\) \(210q^{5} \) \(\mathstrut-\) \(96q^{6} \) \(\mathstrut+\) \(1016q^{7} \) \(\mathstrut-\) \(512q^{8} \) \(\mathstrut-\) \(2043q^{9} \) \(\mathstrut+O(q^{10}) \)